What is the sum from n=1 to infinity of (n^3)/(4^n) ?

The sum from n=1 to infinity of (n^3)/(4^n) is converges

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sum from n=1 to infinity of (n^3)/(4^n)

n = 1 \sum \infty \frac{n ^{3}}{4 ^{n}}

converges

Solution steps

n = 1 \sum \infty \frac{n ^{3}}{4 ^{n}}

Apply Series Ratio Test:

converges

= converges

x \to 1 lim ([g (x) - 3 f (x)])

\int e^{y} d y

\frac{\partial}{\partial y} (e^{y} + x)

f (x) = \frac{5}{x}

x \to 0 lim (e^{3} - e^{x + 3})

What is the sum from n=1 to infinity of (n^3)/(4^n) ?
The sum from n=1 to infinity of (n^3)/(4^n) is converges